sys/sys/tree.h

   1 /*      $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $  */
   2 /*      $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
   3 /*
   4  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   5  * All rights reserved.
   6  *
   7  * Redistribution and use in source and binary forms, with or without
   8  * modification, are permitted provided that the following conditions
   9  * are met:
  10  * 1. Redistributions of source code must retain the above copyright
  11  *    notice, this list of conditions and the following disclaimer.
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in the
  14  *    documentation and/or other materials provided with the distribution.
  15  *
  16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  26  */
  27
  28 #ifndef _SYS_TREE_H_
  29 #define _SYS_TREE_H_
  30
  31 #ifndef _SYS_SPINLOCK_H_
  32 #include <sys/spinlock.h>
  33 #endif
  34
  35 void rb_spin_lock(struct spinlock *spin);
  36 void rb_spin_unlock(struct spinlock *spin);
  37
  38 /*
  39  * This file defines data structures for different types of trees:
  40  * splay trees and red-black trees.
  41  *
  42  * A splay tree is a self-organizing data structure.  Every operation
  43  * on the tree causes a splay to happen.  The splay moves the requested
  44  * node to the root of the tree and partly rebalances it.
  45  *
  46  * This has the benefit that request locality causes faster lookups as
  47  * the requested nodes move to the top of the tree.  On the other hand,
  48  * every lookup causes memory writes.
  49  *
  50  * The Balance Theorem bounds the total access time for m operations
  51  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  52  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  53  *
  54  * A red-black tree is a binary search tree with the node color as an
  55  * extra attribute.  It fulfills a set of conditions:
  56  *      - every search path from the root to a leaf consists of the
  57  *        same number of black nodes,
  58  *      - each red node (except for the root) has a black parent,
  59  *      - each leaf node is black.
  60  *
  61  * Every operation on a red-black tree is bounded as O(lg n).
  62  * The maximum height of a red-black tree is 2lg (n+1).
  63  */
  64
  65 #define SPLAY_HEAD(name, type)                                          \
  66 struct name {                                                           \
  67         struct type *sph_root; /* root of the tree */                   \
  68 }
  69
  70 #define SPLAY_INITIALIZER(root)                                         \
  71         { NULL }
  72
  73 #define SPLAY_INIT(root) do {                                           \
  74         (root)->sph_root = NULL;                                        \
  75 } while (/*CONSTCOND*/ 0)
  76
  77 #define SPLAY_ENTRY(type)                                               \
  78 struct {                                                                \
  79         struct type *spe_left; /* left element */                       \
  80         struct type *spe_right; /* right element */                     \
  81 }
  82
  83 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  84 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  85 #define SPLAY_ROOT(head)                (head)->sph_root
  86 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  87
  88 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  89 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  90         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  91         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  92         (head)->sph_root = tmp;                                         \
  93 } while (/*CONSTCOND*/ 0)
  94
  95 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  96         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  97         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  98         (head)->sph_root = tmp;                                         \
  99 } while (/*CONSTCOND*/ 0)
 100
 101 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
 102         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
 103         tmp = (head)->sph_root;                                         \
 104         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
 105 } while (/*CONSTCOND*/ 0)
 106
 107 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 108         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 109         tmp = (head)->sph_root;                                         \
 110         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 111 } while (/*CONSTCOND*/ 0)
 112
 113 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 114         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 115         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 116         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 117         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 118 } while (/*CONSTCOND*/ 0)
 119
 120 /* Generates prototypes and inline functions */
 121
 122 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 123 void name##_SPLAY(struct name *, struct type *);                        \
 124 void name##_SPLAY_MINMAX(struct name *, int);                           \
 125 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 126 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 127                                                                         \
 128 /* Finds the node with the same key as elm */                           \
 129 static __inline struct type *                                           \
 130 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 131 {                                                                       \
 132         if (SPLAY_EMPTY(head))                                          \
 133                 return(NULL);                                           \
 134         name##_SPLAY(head, elm);                                        \
 135         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 136                 return (head->sph_root);                                \
 137         return (NULL);                                                  \
 138 }                                                                       \
 139                                                                         \
 140 static __inline struct type *                                           \
 141 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 142 {                                                                       \
 143         name##_SPLAY(head, elm);                                        \
 144         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 145                 elm = SPLAY_RIGHT(elm, field);                          \
 146                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 147                         elm = SPLAY_LEFT(elm, field);                   \
 148                 }                                                       \
 149         } else                                                          \
 150                 elm = NULL;                                             \
 151         return (elm);                                                   \
 152 }                                                                       \
 153                                                                         \
 154 static __inline struct type *                                           \
 155 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 156 {                                                                       \
 157         name##_SPLAY_MINMAX(head, val);                                 \
 158         return (SPLAY_ROOT(head));                                      \
 159 }
 160
 161 /* Main splay operation.
 162  * Moves node close to the key of elm to top
 163  */
 164 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 165 struct type *                                                           \
 166 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 167 {                                                                       \
 168     if (SPLAY_EMPTY(head)) {                                            \
 169             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 170     } else {                                                            \
 171             int __comp;                                                 \
 172             name##_SPLAY(head, elm);                                    \
 173             __comp = (cmp)(elm, (head)->sph_root);                      \
 174             if(__comp < 0) {                                            \
 175                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 176                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 177                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 178             } else if (__comp > 0) {                                    \
 179                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 180                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 181                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 182             } else                                                      \
 183                     return ((head)->sph_root);                          \
 184     }                                                                   \
 185     (head)->sph_root = (elm);                                           \
 186     return (NULL);                                                      \
 187 }                                                                       \
 188                                                                         \
 189 struct type *                                                           \
 190 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 191 {                                                                       \
 192         struct type *__tmp;                                             \
 193         if (SPLAY_EMPTY(head))                                          \
 194                 return (NULL);                                          \
 195         name##_SPLAY(head, elm);                                        \
 196         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 197                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 198                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 199                 } else {                                                \
 200                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 201                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 202                         name##_SPLAY(head, elm);                        \
 203                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 204                 }                                                       \
 205                 return (elm);                                           \
 206         }                                                               \
 207         return (NULL);                                                  \
 208 }                                                                       \
 209                                                                         \
 210 void                                                                    \
 211 name##_SPLAY(struct name *head, struct type *elm)                       \
 212 {                                                                       \
 213         struct type __node, *__left, *__right, *__tmp;                  \
 214         int __comp;                                                     \
 215 \
 216         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 217         __left = __right = &__node;                                     \
 218 \
 219         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 220                 if (__comp < 0) {                                       \
 221                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 222                         if (__tmp == NULL)                              \
 223                                 break;                                  \
 224                         if ((cmp)(elm, __tmp) < 0){                     \
 225                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 226                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 227                                         break;                          \
 228                         }                                               \
 229                         SPLAY_LINKLEFT(head, __right, field);           \
 230                 } else if (__comp > 0) {                                \
 231                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 232                         if (__tmp == NULL)                              \
 233                                 break;                                  \
 234                         if ((cmp)(elm, __tmp) > 0){                     \
 235                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 236                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 237                                         break;                          \
 238                         }                                               \
 239                         SPLAY_LINKRIGHT(head, __left, field);           \
 240                 }                                                       \
 241         }                                                               \
 242         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 243 }                                                                       \
 244                                                                         \
 245 /* Splay with either the minimum or the maximum element                 \
 246  * Used to find minimum or maximum element in tree.                     \
 247  */                                                                     \
 248 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 249 {                                                                       \
 250         struct type __node, *__left, *__right, *__tmp;                  \
 251 \
 252         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 253         __left = __right = &__node;                                     \
 254 \
 255         while (1) {                                                     \
 256                 if (__comp < 0) {                                       \
 257                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 258                         if (__tmp == NULL)                              \
 259                                 break;                                  \
 260                         if (__comp < 0){                                \
 261                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 262                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 263                                         break;                          \
 264                         }                                               \
 265                         SPLAY_LINKLEFT(head, __right, field);           \
 266                 } else if (__comp > 0) {                                \
 267                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 268                         if (__tmp == NULL)                              \
 269                                 break;                                  \
 270                         if (__comp > 0) {                               \
 271                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 272                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 273                                         break;                          \
 274                         }                                               \
 275                         SPLAY_LINKRIGHT(head, __left, field);           \
 276                 }                                                       \
 277         }                                                               \
 278         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 279 }
 280
 281 #define SPLAY_NEGINF    -1
 282 #define SPLAY_INF       1
 283
 284 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 285 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 286 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 287 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 288 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 289                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 290 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 291                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 292
 293 #define SPLAY_FOREACH(x, name, head)                                    \
 294         for ((x) = SPLAY_MIN(name, head);                               \
 295              (x) != NULL;                                               \
 296              (x) = SPLAY_NEXT(name, head, x))
 297
 298 /*
 299  * Macros that define a red-black tree
 300  */
 301
 302 #define RB_SCAN_INFO(name, type)                                        \
 303 struct name##_scan_info {                                               \
 304         struct name##_scan_info *link;                                  \
 305         struct type     *node;                                          \
 306 }
 307
 308 #define RB_HEAD(name, type)                                             \
 309 struct name {                                                           \
 310         struct type *rbh_root;               /* root of the tree */     \
 311         struct name##_scan_info *rbh_inprog; /* scans in progress */    \
 312         struct spinlock rbh_spin;                                       \
 313 }
 314
 315 #define RB_INITIALIZER(root)                                            \
 316         { NULL, NULL, SPINLOCK_INITIALIZER(root.spin) }
 317
 318 #define RB_INIT(root) do {                                              \
 319         (root)->rbh_root = NULL;                                        \
 320         (root)->rbh_inprog = NULL;                                      \
 321 } while (/*CONSTCOND*/ 0)
 322
 323 #ifdef _KERNEL
 324 #define RB_SCAN_LOCK(spin)      rb_spin_lock(spin)
 325 #define RB_SCAN_UNLOCK(spin)    rb_spin_unlock(spin)
 326 #else
 327 #define RB_SCAN_LOCK(spin)
 328 #define RB_SCAN_UNLOCK(spin)
 329 #endif
 330
 331 #define RB_BLACK        0
 332 #define RB_RED          1
 333 #define RB_ENTRY(type)                                                  \
 334 struct {                                                                \
 335         struct type *rbe_left;          /* left element */              \
 336         struct type *rbe_right;         /* right element */             \
 337         struct type *rbe_parent;        /* parent element */            \
 338         int rbe_color;                  /* node color */                \
 339 }
 340
 341 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 342 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 343 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 344 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 345 #define RB_ROOT(head)                   (head)->rbh_root
 346 #define RB_INPROG(head)                 (head)->rbh_inprog
 347 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 348
 349 #define RB_SET(elm, parent, field) do {                                 \
 350         RB_PARENT(elm, field) = parent;                                 \
 351         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 352         RB_COLOR(elm, field) = RB_RED;                                  \
 353 } while (/*CONSTCOND*/ 0)
 354
 355 #define RB_SET_BLACKRED(black, red, field) do {                         \
 356         RB_COLOR(black, field) = RB_BLACK;                              \
 357         RB_COLOR(red, field) = RB_RED;                                  \
 358 } while (/*CONSTCOND*/ 0)
 359
 360 #ifndef RB_AUGMENT
 361 #define RB_AUGMENT(x)   do {} while (0)
 362 #endif
 363
 364 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 365         (tmp) = RB_RIGHT(elm, field);                                   \
 366         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 367                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 368         }                                                               \
 369         RB_AUGMENT(elm);                                                \
 370         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 371                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 372                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 373                 else                                                    \
 374                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 375         } else                                                          \
 376                 (head)->rbh_root = (tmp);                               \
 377         RB_LEFT(tmp, field) = (elm);                                    \
 378         RB_PARENT(elm, field) = (tmp);                                  \
 379         RB_AUGMENT(tmp);                                                \
 380         if ((RB_PARENT(tmp, field)))                                    \
 381                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 382 } while (/*CONSTCOND*/ 0)
 383
 384 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 385         (tmp) = RB_LEFT(elm, field);                                    \
 386         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 387                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 388         }                                                               \
 389         RB_AUGMENT(elm);                                                \
 390         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 391                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 392                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 393                 else                                                    \
 394                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 395         } else                                                          \
 396                 (head)->rbh_root = (tmp);                               \
 397         RB_RIGHT(tmp, field) = (elm);                                   \
 398         RB_PARENT(elm, field) = (tmp);                                  \
 399         RB_AUGMENT(tmp);                                                \
 400         if ((RB_PARENT(tmp, field)))                                    \
 401                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 402 } while (/*CONSTCOND*/ 0)
 403
 404 /* Generates prototypes and inline functions */
 405 #define RB_PROTOTYPE(name, type, field, cmp)                            \
 406         _RB_PROTOTYPE(name, type, field, cmp,)
 407 #define RB_PROTOTYPE_STATIC(name, type, field, cmp)                     \
 408         _RB_PROTOTYPE(name, type, field, cmp, __unused static)
 409
 410 #define _RB_PROTOTYPE(name, type, field, cmp, STORQUAL)                 \
 411 STORQUAL void name##_RB_INSERT_COLOR(struct name *, struct type *);     \
 412 STORQUAL void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
 413 STORQUAL struct type *name##_RB_REMOVE(struct name *, struct type *);   \
 414 STORQUAL struct type *name##_RB_INSERT(struct name *, struct type *);   \
 415 STORQUAL struct type *name##_RB_FIND(struct name *, struct type *);     \
 416 STORQUAL int name##_RB_SCAN(struct name *, int (*)(struct type *, void *),\
 417                         int (*)(struct type *, void *), void *);        \
 418 STORQUAL struct type *name##_RB_NEXT(struct type *);                    \
 419 STORQUAL struct type *name##_RB_PREV(struct type *);                    \
 420 STORQUAL struct type *name##_RB_MINMAX(struct name *, int);             \
 421 RB_SCAN_INFO(name, type)                                                \
 422
 423 /*
 424  * A version which supplies a fast lookup routine for an exact match
 425  * on a numeric field.
 426  */
 427 #define RB_PROTOTYPE2(name, type, field, cmp, datatype)                 \
 428 RB_PROTOTYPE(name, type, field, cmp);                                   \
 429 struct type *name##_RB_LOOKUP(struct name *, datatype)                  \
 430
 431 /*
 432  * A version which supplies a fast lookup routine for a numeric
 433  * field which resides within a ranged object, either using (begin,end),
 434  * or using (begin,size).
 435  */
 436 #define RB_PROTOTYPE3(name, type, field, cmp, datatype)                 \
 437 RB_PROTOTYPE2(name, type, field, cmp, datatype);                        \
 438 struct type *name##_RB_RLOOKUP(struct name *, datatype)                 \
 439
 440 #define RB_PROTOTYPE4(name, type, field, cmp, datatype)                 \
 441 RB_PROTOTYPE2(name, type, field, cmp, datatype);                        \
 442 struct type *name##_RB_RLOOKUP(struct name *, datatype)                 \
 443
 444 #define RB_PROTOTYPEX(name, ext, type, field, cmp, datatype)            \
 445 RB_PROTOTYPE(name, type, field, cmp);                                   \
 446 struct type *name##_RB_LOOKUP_##ext (struct name *, datatype)           \
 447
 448 /* Main rb operation.
 449  * Moves node close to the key of elm to top
 450  */
 451 #define RB_GENERATE(name, type, field, cmp)                             \
 452         _RB_GENERATE(name, type, field, cmp,)
 453
 454 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 455         _RB_GENERATE(name, type, field, cmp, __unused static)
 456
 457 #define _RB_GENERATE(name, type, field, cmp, STORQUAL)                  \
 458 void                                                            \
 459 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 460 {                                                                       \
 461         struct type *parent, *gparent, *tmp;                            \
 462         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 463             RB_COLOR(parent, field) == RB_RED) {                        \
 464                 gparent = RB_PARENT(parent, field);                     \
 465                 if (parent == RB_LEFT(gparent, field)) {                \
 466                         tmp = RB_RIGHT(gparent, field);                 \
 467                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 468                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 469                                 RB_SET_BLACKRED(parent, gparent, field);\
 470                                 elm = gparent;                          \
 471                                 continue;                               \
 472                         }                                               \
 473                         if (RB_RIGHT(parent, field) == elm) {           \
 474                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 475                                 tmp = parent;                           \
 476                                 parent = elm;                           \
 477                                 elm = tmp;                              \
 478                         }                                               \
 479                         RB_SET_BLACKRED(parent, gparent, field);        \
 480                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 481                 } else {                                                \
 482                         tmp = RB_LEFT(gparent, field);                  \
 483                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 484                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 485                                 RB_SET_BLACKRED(parent, gparent, field);\
 486                                 elm = gparent;                          \
 487                                 continue;                               \
 488                         }                                               \
 489                         if (RB_LEFT(parent, field) == elm) {            \
 490                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 491                                 tmp = parent;                           \
 492                                 parent = elm;                           \
 493                                 elm = tmp;                              \
 494                         }                                               \
 495                         RB_SET_BLACKRED(parent, gparent, field);        \
 496                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 497                 }                                                       \
 498         }                                                               \
 499         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 500 }                                                                       \
 501                                                                         \
 502 void                                                            \
 503 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent,          \
 504                         struct type *elm)                               \
 505 {                                                                       \
 506         struct type *tmp;                                               \
 507         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 508             elm != RB_ROOT(head)) {                                     \
 509                 if (RB_LEFT(parent, field) == elm) {                    \
 510                         tmp = RB_RIGHT(parent, field);                  \
 511                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 512                                 RB_SET_BLACKRED(tmp, parent, field);    \
 513                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 514                                 tmp = RB_RIGHT(parent, field);          \
 515                         }                                               \
 516                         if ((RB_LEFT(tmp, field) == NULL ||             \
 517                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 518                             (RB_RIGHT(tmp, field) == NULL ||            \
 519                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 520                                 RB_COLOR(tmp, field) = RB_RED;          \
 521                                 elm = parent;                           \
 522                                 parent = RB_PARENT(elm, field);         \
 523                         } else {                                        \
 524                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 525                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 526                                         struct type *oleft;             \
 527                                         if ((oleft = RB_LEFT(tmp, field)) \
 528                                             != NULL)                    \
 529                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 530                                         RB_COLOR(tmp, field) = RB_RED;  \
 531                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 532                                         tmp = RB_RIGHT(parent, field);  \
 533                                 }                                       \
 534                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 535                                 RB_COLOR(parent, field) = RB_BLACK;     \
 536                                 if (RB_RIGHT(tmp, field))               \
 537                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 538                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 539                                 elm = RB_ROOT(head);                    \
 540                                 break;                                  \
 541                         }                                               \
 542                 } else {                                                \
 543                         tmp = RB_LEFT(parent, field);                   \
 544                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 545                                 RB_SET_BLACKRED(tmp, parent, field);    \
 546                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 547                                 tmp = RB_LEFT(parent, field);           \
 548                         }                                               \
 549                         if ((RB_LEFT(tmp, field) == NULL ||             \
 550                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 551                             (RB_RIGHT(tmp, field) == NULL ||            \
 552                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 553                                 RB_COLOR(tmp, field) = RB_RED;          \
 554                                 elm = parent;                           \
 555                                 parent = RB_PARENT(elm, field);         \
 556                         } else {                                        \
 557                                 if (RB_LEFT(tmp, field) == NULL ||      \
 558                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 559                                         struct type *oright;            \
 560                                         if ((oright = RB_RIGHT(tmp, field)) \
 561                                             != NULL)                    \
 562                                                 RB_COLOR(oright, field) = RB_BLACK;\
 563                                         RB_COLOR(tmp, field) = RB_RED;  \
 564                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 565                                         tmp = RB_LEFT(parent, field);   \
 566                                 }                                       \
 567                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 568                                 RB_COLOR(parent, field) = RB_BLACK;     \
 569                                 if (RB_LEFT(tmp, field))                \
 570                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 571                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 572                                 elm = RB_ROOT(head);                    \
 573                                 break;                                  \
 574                         }                                               \
 575                 }                                                       \
 576         }                                                               \
 577         if (elm)                                                        \
 578                 RB_COLOR(elm, field) = RB_BLACK;                        \
 579 }                                                                       \
 580                                                                         \
 581 STORQUAL struct type *                                                  \
 582 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 583 {                                                                       \
 584         struct type *child, *parent, *old;                              \
 585         struct name##_scan_info *inprog;                                \
 586         int color;                                                      \
 587                                                                         \
 588         for (inprog = RB_INPROG(head); inprog; inprog = inprog->link) { \
 589                 if (inprog->node == elm)                                \
 590                         inprog->node = RB_NEXT(name, head, elm);        \
 591         }                                                               \
 592                                                                         \
 593         old = elm;                                                      \
 594         if (RB_LEFT(elm, field) == NULL)                                \
 595                 child = RB_RIGHT(elm, field);                           \
 596         else if (RB_RIGHT(elm, field) == NULL)                          \
 597                 child = RB_LEFT(elm, field);                            \
 598         else {                                                          \
 599                 struct type *left;                                      \
 600                 elm = RB_RIGHT(elm, field);                             \
 601                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 602                         elm = left;                                     \
 603                 child = RB_RIGHT(elm, field);                           \
 604                 parent = RB_PARENT(elm, field);                         \
 605                 color = RB_COLOR(elm, field);                           \
 606                 if (child)                                              \
 607                         RB_PARENT(child, field) = parent;               \
 608                 if (parent) {                                           \
 609                         if (RB_LEFT(parent, field) == elm)              \
 610                                 RB_LEFT(parent, field) = child;         \
 611                         else                                            \
 612                                 RB_RIGHT(parent, field) = child;        \
 613                         RB_AUGMENT(parent);                             \
 614                 } else                                                  \
 615                         RB_ROOT(head) = child;                          \
 616                 if (RB_PARENT(elm, field) == old)                       \
 617                         parent = elm;                                   \
 618                 (elm)->field = (old)->field;                            \
 619                 if (RB_PARENT(old, field)) {                            \
 620                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 621                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 622                         else                                            \
 623                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 624                         RB_AUGMENT(RB_PARENT(old, field));              \
 625                 } else                                                  \
 626                         RB_ROOT(head) = elm;                            \
 627                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 628                 if (RB_RIGHT(old, field))                               \
 629                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 630                 if (parent) {                                           \
 631                         left = parent;                                  \
 632                         do {                                            \
 633                                 RB_AUGMENT(left);                       \
 634                         } while ((left = RB_PARENT(left, field)) != NULL); \
 635                 }                                                       \
 636                 goto color;                                             \
 637         }                                                               \
 638         parent = RB_PARENT(elm, field);                                 \
 639         color = RB_COLOR(elm, field);                                   \
 640         if (child)                                                      \
 641                 RB_PARENT(child, field) = parent;                       \
 642         if (parent) {                                                   \
 643                 if (RB_LEFT(parent, field) == elm)                      \
 644                         RB_LEFT(parent, field) = child;                 \
 645                 else                                                    \
 646                         RB_RIGHT(parent, field) = child;                \
 647                 RB_AUGMENT(parent);                                     \
 648         } else                                                          \
 649                 RB_ROOT(head) = child;                                  \
 650 color:                                                                  \
 651         if (color == RB_BLACK)                                          \
 652                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 653         return (old);                                                   \
 654 }                                                                       \
 655                                                                         \
 656 /* Inserts a node into the RB tree */                                   \
 657 STORQUAL struct type *                                                  \
 658 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 659 {                                                                       \
 660         struct type *tmp;                                               \
 661         struct type *parent = NULL;                                     \
 662         int comp = 0;                                                   \
 663         tmp = RB_ROOT(head);                                            \
 664         while (tmp) {                                                   \
 665                 parent = tmp;                                           \
 666                 comp = (cmp)(elm, parent);                              \
 667                 if (comp < 0)                                           \
 668                         tmp = RB_LEFT(tmp, field);                      \
 669                 else if (comp > 0)                                      \
 670                         tmp = RB_RIGHT(tmp, field);                     \
 671                 else                                                    \
 672                         return(tmp);                                    \
 673         }                                                               \
 674         RB_SET(elm, parent, field);                                     \
 675         if (parent != NULL) {                                           \
 676                 if (comp < 0)                                           \
 677                         RB_LEFT(parent, field) = elm;                   \
 678                 else                                                    \
 679                         RB_RIGHT(parent, field) = elm;                  \
 680                 RB_AUGMENT(parent);                                     \
 681         } else                                                          \
 682                 RB_ROOT(head) = elm;                                    \
 683         name##_RB_INSERT_COLOR(head, elm);                              \
 684         return (NULL);                                                  \
 685 }                                                                       \
 686                                                                         \
 687 /* Finds the node with the same key as elm */                           \
 688 STORQUAL struct type *                                                  \
 689 name##_RB_FIND(struct name *head, struct type *elm)                     \
 690 {                                                                       \
 691         struct type *tmp = RB_ROOT(head);                               \
 692         int comp;                                                       \
 693         while (tmp) {                                                   \
 694                 comp = cmp(elm, tmp);                                   \
 695                 if (comp < 0)                                           \
 696                         tmp = RB_LEFT(tmp, field);                      \
 697                 else if (comp > 0)                                      \
 698                         tmp = RB_RIGHT(tmp, field);                     \
 699                 else                                                    \
 700                         return (tmp);                                   \
 701         }                                                               \
 702         return (NULL);                                                  \
 703 }                                                                       \
 704                                                                         \
 705 /*                                                                      \
 706  * Issue a callback for all matching items.  The scan function must     \
 707  * return < 0 for items below the desired range, 0 for items within     \
 708  * the range, and > 0 for items beyond the range.   Any item may be     \
 709  * deleted while the scan is in progress.                               \
 710  */                                                                     \
 711 static int                                                              \
 712 name##_SCANCMP_ALL(struct type *type __unused, void *data __unused)     \
 713 {                                                                       \
 714         return(0);                                                      \
 715 }                                                                       \
 716                                                                         \
 717 static __inline void                                                    \
 718 name##_scan_info_link(struct name##_scan_info *scan, struct name *head) \
 719 {                                                                       \
 720         RB_SCAN_LOCK(&head->rbh_spin);                                  \
 721         scan->link = RB_INPROG(head);                                   \
 722         RB_INPROG(head) = scan;                                         \
 723         RB_SCAN_UNLOCK(&head->rbh_spin);                                \
 724 }                                                                       \
 725                                                                         \
 726 static __inline void                                                    \
 727 name##_scan_info_done(struct name##_scan_info *scan, struct name *head) \
 728 {                                                                       \
 729         struct name##_scan_info **infopp;                               \
 730                                                                         \
 731         RB_SCAN_LOCK(&head->rbh_spin);                                  \
 732         infopp = &RB_INPROG(head);                                      \
 733         while (*infopp != scan)                                         \
 734                 infopp = &(*infopp)->link;                              \
 735         *infopp = scan->link;                                           \
 736         RB_SCAN_UNLOCK(&head->rbh_spin);                                \
 737 }                                                                       \
 738                                                                         \
 739 STORQUAL int                                                            \
 740 name##_RB_SCAN(struct name *head,                                       \
 741                 int (*scancmp)(struct type *, void *),                  \
 742                 int (*callback)(struct type *, void *),                 \
 743                 void *data)                                             \
 744 {                                                                       \
 745         struct name##_scan_info info;                                   \
 746         struct type *best;                                              \
 747         struct type *tmp;                                               \
 748         int count;                                                      \
 749         int comp;                                                       \
 750                                                                         \
 751         if (scancmp == NULL)                                            \
 752                 scancmp = name##_SCANCMP_ALL;                           \
 753                                                                         \
 754         /*                                                              \
 755          * Locate the first element.                                    \
 756          */                                                             \
 757         tmp = RB_ROOT(head);                                            \
 758         best = NULL;                                                    \
 759         while (tmp) {                                                   \
 760                 comp = scancmp(tmp, data);                              \
 761                 if (comp < 0) {                                         \
 762                         tmp = RB_RIGHT(tmp, field);                     \
 763                 } else if (comp > 0) {                                  \
 764                         tmp = RB_LEFT(tmp, field);                      \
 765                 } else {                                                \
 766                         best = tmp;                                     \
 767                         if (RB_LEFT(tmp, field) == NULL)                \
 768                                 break;                                  \
 769                         tmp = RB_LEFT(tmp, field);                      \
 770                 }                                                       \
 771         }                                                               \
 772         count = 0;                                                      \
 773         if (best) {                                                     \
 774                 info.node = RB_NEXT(name, head, best);                  \
 775                 name##_scan_info_link(&info, head);                     \
 776                 while ((comp = callback(best, data)) >= 0) {            \
 777                         count += comp;                                  \
 778                         best = info.node;                               \
 779                         if (best == NULL || scancmp(best, data) != 0)   \
 780                                 break;                                  \
 781                         info.node = RB_NEXT(name, head, best);          \
 782                 }                                                       \
 783                 name##_scan_info_done(&info, head);                     \
 784                 if (comp < 0)   /* error or termination */              \
 785                         count = comp;                                   \
 786         }                                                               \
 787         return(count);                                                  \
 788 }                                                                       \
 789                                                                         \
 790 /* ARGSUSED */                                                          \
 791 STORQUAL struct type *                                                  \
 792 name##_RB_NEXT(struct type *elm)                                        \
 793 {                                                                       \
 794         if (RB_RIGHT(elm, field)) {                                     \
 795                 elm = RB_RIGHT(elm, field);                             \
 796                 while (RB_LEFT(elm, field))                             \
 797                         elm = RB_LEFT(elm, field);                      \
 798         } else {                                                        \
 799                 if (RB_PARENT(elm, field) &&                            \
 800                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 801                         elm = RB_PARENT(elm, field);                    \
 802                 else {                                                  \
 803                         while (RB_PARENT(elm, field) &&                 \
 804                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 805                                 elm = RB_PARENT(elm, field);            \
 806                         elm = RB_PARENT(elm, field);                    \
 807                 }                                                       \
 808         }                                                               \
 809         return (elm);                                                   \
 810 }                                                                       \
 811                                                                         \
 812 /* ARGSUSED */                                                          \
 813 STORQUAL struct type *                                                  \
 814 name##_RB_PREV(struct type *elm)                                        \
 815 {                                                                       \
 816         if (RB_LEFT(elm, field)) {                                      \
 817                 elm = RB_LEFT(elm, field);                              \
 818                 while (RB_RIGHT(elm, field))                            \
 819                         elm = RB_RIGHT(elm, field);                     \
 820         } else {                                                        \
 821                 if (RB_PARENT(elm, field) &&                            \
 822                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 823                         elm = RB_PARENT(elm, field);                    \
 824                 else {                                                  \
 825                         while (RB_PARENT(elm, field) &&                 \
 826                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 827                                 elm = RB_PARENT(elm, field);            \
 828                         elm = RB_PARENT(elm, field);                    \
 829                 }                                                       \
 830         }                                                               \
 831         return (elm);                                                   \
 832 }                                                                       \
 833                                                                         \
 834 STORQUAL struct type *                                                  \
 835 name##_RB_MINMAX(struct name *head, int val)                            \
 836 {                                                                       \
 837         struct type *tmp = RB_ROOT(head);                               \
 838         struct type *parent = NULL;                                     \
 839         while (tmp) {                                                   \
 840                 parent = tmp;                                           \
 841                 if (val < 0)                                            \
 842                         tmp = RB_LEFT(tmp, field);                      \
 843                 else                                                    \
 844                         tmp = RB_RIGHT(tmp, field);                     \
 845         }                                                               \
 846         return (parent);                                                \
 847 }
 848
 849 /*
 850  * This extended version implements a fast LOOKUP function given
 851  * a numeric data type.
 852  *
 853  * The element whos index/offset field is exactly the specified value
 854  * will be returned, or NULL.
 855  */
 856 #define RB_GENERATE2(name, type, field, cmp, datatype, indexfield)      \
 857 RB_GENERATE(name, type, field, cmp)                                     \
 858                                                                         \
 859 struct type *                                                           \
 860 name##_RB_LOOKUP(struct name *head, datatype value)                     \
 861 {                                                                       \
 862         struct type *tmp;                                               \
 863                                                                         \
 864         tmp = RB_ROOT(head);                                            \
 865         while (tmp) {                                                   \
 866                 if (value > tmp->indexfield)                            \
 867                         tmp = RB_RIGHT(tmp, field);                     \
 868                 else if (value < tmp->indexfield)                       \
 869                         tmp = RB_LEFT(tmp, field);                      \
 870                 else                                                    \
 871                         return(tmp);                                    \
 872         }                                                               \
 873         return(NULL);                                                   \
 874 }                                                                       \
 875
 876 /*
 877  * This extended version implements a fast ranged-based LOOKUP function
 878  * given a numeric data type, for data types with a beginning and end
 879  * (end is inclusive).
 880  *
 881  * The element whos range contains the specified value is returned, or NULL
 882  */
 883 #define RB_GENERATE3(name, type, field, cmp, datatype, begfield, endfield) \
 884 RB_GENERATE2(name, type, field, cmp, datatype, begfield)                \
 885                                                                         \
 886 struct type *                                                           \
 887 name##_RB_RLOOKUP(struct name *head, datatype value)                    \
 888 {                                                                       \
 889         struct type *tmp;                                               \
 890                                                                         \
 891         tmp = RB_ROOT(head);                                            \
 892         while (tmp) {                                                   \
 893                 if (value >= tmp->begfield && value <= tmp->endfield)   \
 894                         return(tmp);                                    \
 895                 if (value > tmp->begfield)                              \
 896                         tmp = RB_RIGHT(tmp, field);                     \
 897                 else                                                    \
 898                         tmp = RB_LEFT(tmp, field);                      \
 899         }                                                               \
 900         return(NULL);                                                   \
 901 }                                                                       \
 902
 903 /*
 904  * This extended version implements a fast ranged-based LOOKUP function
 905  * given a numeric data type, for data types with a beginning and size.
 906  *
 907  * WARNING: The full range of the data type is not supported due to a
 908  * boundary condition at the end, where (beginning + size) might overflow.
 909  *
 910  * The element whos range contains the specified value is returned, or NULL
 911  */
 912 #define RB_GENERATE4(name, type, field, cmp, datatype, begfield, sizefield) \
 913 RB_GENERATE2(name, type, field, cmp, datatype, begfield)                \
 914                                                                         \
 915 struct type *                                                           \
 916 name##_RB_RLOOKUP(struct name *head, datatype value)                    \
 917 {                                                                       \
 918         struct type *tmp;                                               \
 919                                                                         \
 920         tmp = RB_ROOT(head);                                            \
 921         while (tmp) {                                                   \
 922                 if (value >= tmp->begfield &&                           \
 923                     value < tmp->begfield + tmp->sizefield) {           \
 924                         return(tmp);                                    \
 925                 }                                                       \
 926                 if (value > tmp->begfield)                              \
 927                         tmp = RB_RIGHT(tmp, field);                     \
 928                 else                                                    \
 929                         tmp = RB_LEFT(tmp, field);                      \
 930         }                                                               \
 931         return(NULL);                                                   \
 932 }                                                                       \
 933
 934 /*
 935  * This generates a custom lookup function for a red-black tree.
 936  * Note that the macro may be used with a storage qualifier.
 937  */
 938
 939 #define RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype)        \
 940         _RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype,)
 941 #define RB_GENERATE_XLOOKUP_STATIC(name, ext, type, field, xcmp, datatype) \
 942         _RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype, __unused static)
 943
 944 #define _RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype, STORQUAL)\
 945                                                                         \
 946 STORQUAL struct type *                                                  \
 947 name##_RB_LOOKUP_##ext (struct name *head, datatype value)              \
 948 {                                                                       \
 949         struct type *tmp;                                               \
 950         int r;                                                          \
 951                                                                         \
 952         tmp = RB_ROOT(head);                                            \
 953         while (tmp) {                                                   \
 954                 r = xcmp(value, tmp);                                   \
 955                 if (r == 0)                                             \
 956                         return(tmp);                                    \
 957                 if (r > 0)                                              \
 958                         tmp = RB_RIGHT(tmp, field);                     \
 959                 else                                                    \
 960                         tmp = RB_LEFT(tmp, field);                      \
 961         }                                                               \
 962         return(NULL);                                                   \
 963 }                                                                       \
 964
 965
 966 #define RB_NEGINF       -1
 967 #define RB_INF  1
 968
 969 #define RB_INSERT(name, root, elm)      name##_RB_INSERT(root, elm)
 970 #define RB_REMOVE(name, root, elm)      name##_RB_REMOVE(root, elm)
 971 #define RB_FIND(name, root, elm)        name##_RB_FIND(root, elm)
 972 #define RB_LOOKUP(name, root, value)    name##_RB_LOOKUP(root, value)
 973 #define RB_RLOOKUP(name, root, value)   name##_RB_RLOOKUP(root, value)
 974 #define RB_SCAN(name, root, cmp, callback, data)                        \
 975                                 name##_RB_SCAN(root, cmp, callback, data)
 976 #define RB_FIRST(name, root)            name##_RB_MINMAX(root, RB_NEGINF)
 977 #define RB_NEXT(name, root, elm)        name##_RB_NEXT(elm)
 978 #define RB_PREV(name, root, elm)        name##_RB_PREV(elm)
 979 #define RB_MIN(name, root)              name##_RB_MINMAX(root, RB_NEGINF)
 980 #define RB_MAX(name, root)              name##_RB_MINMAX(root, RB_INF)
 981
 982 #define RB_FOREACH(x, name, head)                                       \
 983         for ((x) = RB_MIN(name, head);                                  \
 984              (x) != NULL;                                               \
 985              (x) = name##_RB_NEXT(x))
 986
 987 #endif  /* _SYS_TREE_H_ */